Three-way component analysis: principles and illustrative application

Three-way component analysis techniques are designed for descriptive analysis of 3-way data, for example, when data are collected on individuals, in different settings, and on different measures. Such techniques summarize all information in a 3-way data set by summarizing, for each way of the 3-way data set, the associated entities through a few components and describing the relations between these components. In this article, 3-mode principal components analysis is described at an elementary level. Guidance is given concerning the choices to be made in each step of the process of analyzing 3-way data by this technique. The complete process is illustrated with a detailed description of the analysis of an empirical 3-way data set.